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<p>&#x5047;&#x8BBE;&#x6709;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">n</span></span></span></span>&#x79CD;&#x53EF;&#x80FD;&#x7684;&#x7C7B;&#x522B;&#x6807;&#x8BB0;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">Y</mi><mo>=</mo><mo stretchy="false">{</mo><msub><mi>c</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>c</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>&#x22EF;</mo><mtext>&#x2009;</mtext><mo separator="true">,</mo><msub><mi>c</mi><mi>n</mi></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\mathcal{Y}=\{c_1,c_2,\cdots,c_n\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78055em;vertical-align:-0.09722em;"></span><span class="mord"><span class="mord mathcal" style="margin-right:0.08222em;">Y</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">&#x22EF;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span>&#xFF0C;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>&#x3BB;</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">&#x3BB;_{ij}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathdefault">&#x3BB;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>&#x662F;&#x5C06;&#x4E00;&#x4E2A;&#x771F;&#x5B9E;&#x6807;&#x8BB0;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">c_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>&#x7684;&#x6837;&#x672C;&#x5206;&#x4E3A;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">c_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>&#x6240;&#x4EA7;&#x751F;&#x7684;&#x635F;&#x5931;&#x3002;</p>
<h3 class="mume-header" id="%E6%9D%A1%E4%BB%B6%E9%A3%8E%E9%99%A9conditional-risk">&#x6761;&#x4EF6;&#x98CE;&#x9669;&#xFF08;Conditional Risk&#xFF09;</h3>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo stretchy="false">(</mo><msub><mi>c</mi><mi>i</mi></msub><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><munderover><mo>&#x2211;</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>&#x3BB;</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mi>P</mi><mo stretchy="false">(</mo><msub><mi>c</mi><mi>i</mi></msub><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">R(c_i \bold{\ |\ } x) = \sum_{j=1}^{n} &#x3BB;_{ij} P(c_i \bold{\ |\ } x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.0651740000000007em;vertical-align:-1.4137769999999998em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6513970000000007em;"><span style="top:-1.872331em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.4137769999999998em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault">&#x3BB;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span></span></p>
<p>&#x8BE5;&#x5F0F;&#x53CD;&#x6620;&#x4E86;&#x5C06;&#x6837;&#x672C;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">x</span></span></span></span>&#x5206;&#x7C7B;&#x5230;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">c_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>&#x4EA7;&#x751F;&#x7684;&#x98CE;&#x9669;&#x3002;</p>
<h3 class="mume-header" id="%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%88%A4%E5%AE%9A%E5%87%86%E5%88%99">&#x8D1D;&#x53F6;&#x65AF;&#x5224;&#x5B9A;&#x51C6;&#x5219;</h3>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>h</mi><mo>&#x2217;</mo></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><munder><mo><mi mathvariant="normal">arg&#x2009;min</mi><mo>&#x2061;</mo></mo><mrow><mi>c</mi><mo>&#x2208;</mo><mi mathvariant="script">Y</mi></mrow></munder><mi>R</mi><mo stretchy="false">(</mo><mi>c</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">h^*(x) = \argmin_{c&#x2208;\mathcal{Y}} R(c \bold{\ |\ } x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.738696em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">&#x2217;</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.7568249999999999em;vertical-align:-1.0068249999999999em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6678600000000001em;"><span style="top:-2.161229em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mrel mtight">&#x2208;</span><span class="mord mtight"><span class="mord mathcal mtight" style="margin-right:0.08222em;">Y</span></span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop"><span class="mord mathrm">a</span><span class="mord mathrm">r</span><span class="mord mathrm" style="margin-right:0.01389em;">g</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathrm">m</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.0068249999999999em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span></span></p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">X</mi><munderover><mo stretchy="true">&#x2192;</mo><mpadded width="+0.6em" lspace="0.3em"><mrow></mrow></mpadded><mpadded width="+0.6em" lspace="0.3em"><mi>h</mi></mpadded></munderover><mi mathvariant="script">Y</mi></mrow><annotation encoding="application/x-tex">\mathcal{X} \xrightarrow[]{h} \mathcal{Y}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.230108em;vertical-align:-0.12200000000000011em;"></span><span class="mord"><span class="mord mathcal" style="margin-right:0.14643em;">X</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel x-arrow"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1081079999999999em;"><span style="top:-3.322em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight x-arrow-pad"><span class="mord mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="svg-align" style="top:-2.689em;"><span class="pstrut" style="height:2.7em;"></span><span class="hide-tail" style="height:0.522em;min-width:1.469em;"><svg width="400em" height="0.522em" viewBox="0 0 400000 522" preserveAspectRatio="xMaxYMin slice"><path d="M0 241v40h399891c-47.3 35.3-84 78-110 128
-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20
 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7
 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85
-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5
-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67
 151.7 139 205zm0 0v40h399900v-40z"/></svg></span></span><span style="top:-2.5780000000000003em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight x-arrow-pad"><span class="mord mtight"></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.12200000000000011em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.78055em;vertical-align:-0.09722em;"></span><span class="mord"><span class="mord mathcal" style="margin-right:0.08222em;">Y</span></span></span></span></span></li>
</ul>
<p>&#x5373;&#x6620;&#x5C04;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">h</span></span></span></span>&#x53EF;&#x4EE5;&#x4F7F;&#x6BCF;&#x4E2A;&#x6837;&#x672C;&#x7684;&#x7684;&#x6761;&#x4EF6;&#x98CE;&#x9669;&#x90FD;&#x6700;&#x5C0F;&#xFF0C;&#x6B64;&#x65F6;&#x7684;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>h</mi><mo>&#x2217;</mo></msup></mrow><annotation encoding="application/x-tex">h^*</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.688696em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">&#x2217;</span></span></span></span></span></span></span></span></span></span></span>&#x79F0;&#x4E3A;<strong>&#x8D1D;&#x53F6;&#x65AF;&#x6700;&#x4F18;&#x5206;&#x7C7B;&#x5668;</strong>&#xFF0C;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo stretchy="false">(</mo><msup><mi>h</mi><mo>&#x2217;</mo></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">R(h^*)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.688696em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">&#x2217;</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>&#x79F0;&#x4E3A;<strong>&#x8D1D;&#x53F6;&#x65AF;&#x98CE;&#x9669;</strong>&#x3002;</p>
<p><strong>&#x8BE5;&#x5F0F;&#x8FD8;&#x53CD;&#x6620;&#x4E86;&#x901A;&#x8FC7;&#x673A;&#x5668;&#x5B66;&#x4E60;&#x4EA7;&#x751F;&#x7684;&#x6A21;&#x578B;&#x7CBE;&#x5EA6;&#x7684;&#x7406;&#x8BBA;&#x4E0A;&#x9650;&#x3002;</strong></p>
<h3 class="mume-header" id="%E6%9C%80%E5%B0%8F%E5%8C%96%E5%88%86%E7%B1%BB%E9%94%99%E8%AF%AF%E7%8E%87">&#x6700;&#x5C0F;&#x5316;&#x5206;&#x7C7B;&#x9519;&#x8BEF;&#x7387;</h3>

<p>&#x5F53;&#x76EE;&#x6807;&#x662F;&#x6700;&#x5C0F;&#x5316;&#x5206;&#x7C7B;&#x9519;&#x8BEF;&#x7387;&#x65F6;</p>
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>&#x3BB;</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>i</mi><mo>=</mo><mi>j</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>i</mi><mo mathvariant="normal">&#x2260;</mo><mi>j</mi></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">&#x3BB;_{ij} = \begin{cases}
    0 &amp; i=j
\\  1 &amp; i&#x2260;j
\end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathdefault">&#x3BB;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em;"><span style="top:-3.69em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em;"><span style="top:-3.69em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel"><span class="mrel"><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="rlap"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="inner"><span class="mrel">&#xE020;</span></span><span class="fix"></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span><span class="mrel">=</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>c</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>&#x2212;</mo><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">R(c \bold{\ |\ } x) = 1 - P(c \bold{\ |\ } x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span></p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>h</mi><mo>&#x2217;</mo></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><munder><mo><mi mathvariant="normal">arg&#x2009;max</mi><mo>&#x2061;</mo></mo><mrow><mi>c</mi><mo>&#x2208;</mo><mi mathvariant="script">Y</mi></mrow></munder><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">h^*(x) = \argmax\limits_{c&#x2208;\mathcal{Y}} P(c \bold{\ |\ } x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.738696em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">&#x2217;</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.756825em;vertical-align:-1.006825em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.43055999999999983em;"><span style="top:-2.161229em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mrel mtight">&#x2208;</span><span class="mord mtight"><span class="mord mathcal mtight" style="margin-right:0.08222em;">Y</span></span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop"><span class="mord mathrm">a</span><span class="mord mathrm">r</span><span class="mord mathrm" style="margin-right:0.01389em;">g</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathrm">m</span><span class="mord mathrm">a</span><span class="mord mathrm">x</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.006825em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span></span></p>
<h3 class="mume-header" id="%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%88%86%E7%B1%BB%E5%99%A8">&#x8D1D;&#x53F6;&#x65AF;&#x5206;&#x7C7B;&#x5668;</h3>

<p>&#x4E0E;&#x51B3;&#x7B56;&#x6811;&#x3001;SVM&#x3001;BP&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x7B49;<strong>&#x5224;&#x522B;&#x5F0F;&#x6A21;&#x578B;</strong>&#x4E0D;&#x540C;&#x8D1D;&#x53F6;&#x65AF;&#x5206;&#x7C7B;&#x5668;&#x5C5E;&#x4E8E;<strong>&#x751F;&#x6210;&#x5F0F;&#x6A21;&#x578B;</strong>&#x3002;</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>c</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>c</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">P(c \bold{\ |\ } x) 
    = \dfrac{P(x,c)} {P(x)}
    = \dfrac{P(c) &#x22C5; P(x \bold{\ |\ } c)} {P(x)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">c</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">c</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<table>
<thead>
<tr>
<th style="text-align:center">&#x5148;&#x9A8C;&#x6982;&#x7387;</th>
<th style="text-align:center">&#x540E;&#x9A8C;&#x6982;&#x7387;</th>
<th style="text-align:center">&#x8BC1;&#x636E;</th>
<th style="text-align:center">&#x4F3C;&#x7136;&#xFF08;&#x7C7B;&#x6761;&#x4EF6;&#x6982;&#x7387;&#xFF09;</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(c)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mclose">)</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(c \bold{\ \vert\ } x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>c</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(x \bold{\ \vert\ } c)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">c</span><span class="mclose">)</span></span></span></span></td>
</tr>
</tbody>
</table>
<h2 class="mume-header" id="%E6%9E%81%E5%A4%A7%E4%BC%BC%E7%84%B6%E4%BC%B0%E8%AE%A1mle">&#x6781;&#x5927;&#x4F3C;&#x7136;&#x4F30;&#x8BA1;&#xFF08;MLE&#xFF09;</h2>

<p>&#x4EE4;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mi>c</mi></msub></mrow><annotation encoding="application/x-tex">D_c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>&#x8868;&#x793A;&#x8BAD;&#x7EC3;&#x96C6;&#x4E2D;&#x7B2C;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi></mrow><annotation encoding="application/x-tex">c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">c</span></span></span></span>&#x7C7B;&#x6837;&#x672C;&#x7684;&#x96C6;&#x5408;&#xFF0C;&#x5219;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>&#x3B8;</mi><mi>c</mi></msub></mrow><annotation encoding="application/x-tex">&#x3B8;_c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">&#x3B8;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>&#x5BF9;&#x4E8E;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mi>c</mi></msub></mrow><annotation encoding="application/x-tex">D_c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>&#x4F3C;&#x7136;&#x4E3A;</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>D</mi><mi>c</mi></msub><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><msub><mi>&#x3B8;</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mo>=</mo><munder><mo>&#x220F;</mo><mrow><mi>x</mi><mo>&#x2208;</mo><msub><mi>D</mi><mi>c</mi></msub></mrow></munder><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><msub><mi>&#x3B8;</mi><mi>c</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(D_c \bold{\ |\ } &#x3B8;_c) = \prod_{x&#x2208;D_c} P(x \bold{\ |\ } &#x3B8;_c)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">&#x3B8;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.4444410000000003em;vertical-align:-1.394436em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.855664em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="mrel mtight">&#x2208;</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em;"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x220F;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.394436em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">&#x3B8;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p>
<p>&#x4E0A;&#x5F0F;&#x8FDE;&#x4E58;&#x6613;&#x9020;&#x6210;&#x4E0B;&#x6EA2;&#xFF0C;&#x6545;&#x6539;&#x5199;&#x6210;&#x5BF9;&#x6570;&#x4F3C;&#x7136;</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>L</mi><mo stretchy="false">(</mo><msub><mi>&#x3B8;</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>log</mi><mo>&#x2061;</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>D</mi><mi>c</mi></msub><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><msub><mi>&#x3B8;</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mo>=</mo><munder><mo>&#x2211;</mo><mrow><mi>x</mi><mo>&#x2208;</mo><msub><mi>D</mi><mi>c</mi></msub></mrow></munder><mi>log</mi><mo>&#x2061;</mo><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><msub><mi>&#x3B8;</mi><mi>c</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">LL(&#x3B8;_c) 
    = \log P(D_c \bold{\ |\ } &#x3B8;_c) 
    = \sum_{x&#x2208;D_c} \log P(x \bold{\ |\ } &#x3B8;_c)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">L</span><span class="mord mathdefault">L</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">&#x3B8;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">&#x3B8;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.4444410000000003em;vertical-align:-1.394436em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.855664em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="mrel mtight">&#x2208;</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em;"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.394436em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">&#x3B8;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p>
<p>&#x5219;&#x6781;&#x5927;&#x4F3C;&#x7136;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>&#x3B8;</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{&#x3B8;}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9578799999999998em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9578799999999998em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">&#x3B8;</span></span></span><span style="top:-3.26344em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.16666em;"><span class="mord">^</span></span></span></span></span></span></span></span></span></span>&#x4E3A;</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>&#x3B8;</mi><mo>^</mo></mover><mo>=</mo><munder><mo><mi mathvariant="normal">arg&#x2009;max</mi><mo>&#x2061;</mo></mo><msub><mi>&#x3B8;</mi><mi>c</mi></msub></munder><mi>L</mi><mi>L</mi><mo stretchy="false">(</mo><msub><mi>&#x3B8;</mi><mi>c</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\hat{&#x3B8;} = \argmax_{&#x3B8;_c} LL(&#x3B8;_c)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9578799999999998em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9578799999999998em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">&#x3B8;</span></span></span><span style="top:-3.26344em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.16666em;"><span class="mord">^</span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.796648em;vertical-align:-1.046648em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.43055999999999994em;"><span style="top:-2.1534519999999997em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">&#x3B8;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em;"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop"><span class="mord mathrm">a</span><span class="mord mathrm">r</span><span class="mord mathrm" style="margin-right:0.01389em;">g</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathrm">m</span><span class="mord mathrm">a</span><span class="mord mathrm">x</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.046648em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">L</span><span class="mord mathdefault">L</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">&#x3B8;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p>
<p>&#x5728;&#x8FDE;&#x7EED;&#x5C5E;&#x6027;&#x60C5;&#x5F62;&#x4E0B;&#xFF0C;&#x5047;&#x8BBE;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>c</mi><mo stretchy="false">)</mo><mo>&#x223C;</mo><mi>N</mi><mo stretchy="false">(</mo><msub><mi>&#x3BC;</mi><mi>c</mi></msub><mo separator="true">,</mo><msubsup><mi>&#x3C3;</mi><mi>c</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p(x \bold{\ |\ } c)&#x223C;N(&#x3BC;_c, &#x3C3;_c^2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x223C;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">&#x3BC;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">&#x3C3;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>&#xFF0C;&#x5373;&#x6B63;&#x6001;&#x5206;&#x5E03;</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mover accent="true"><mi>&#x3BC;</mi><mo>^</mo></mover><mi>c</mi></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi mathvariant="normal">&#x2223;</mi><msub><mi>D</mi><mi>c</mi></msub><mi mathvariant="normal">&#x2223;</mi></mrow></mfrac></mstyle><munder><mo>&#x2211;</mo><mrow><mi>x</mi><mo>&#x2208;</mo><msub><mi>D</mi><mi>c</mi></msub></mrow></munder><mi>x</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msubsup><mover accent="true"><mi>&#x3C3;</mi><mo>^</mo></mover><mi>c</mi><mn>2</mn></msubsup><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi mathvariant="normal">&#x2223;</mi><msub><mi>D</mi><mi>c</mi></msub><mi mathvariant="normal">&#x2223;</mi></mrow></mfrac></mstyle><munder><mo>&#x2211;</mo><mrow><mi>x</mi><mo>&#x2208;</mo><msub><mi>D</mi><mi>c</mi></msub></mrow></munder><mo stretchy="false">(</mo><mi>x</mi><mo>&#x2212;</mo><msub><mover accent="true"><mi>&#x3BC;</mi><mo>^</mo></mover><mi>c</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&#x2212;</mo><msub><mover accent="true"><mi>&#x3BC;</mi><mo>^</mo></mover><mi>c</mi></msub><msup><mo stretchy="false">)</mo><mi>T</mi></msup></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases}
    \hat{&#x3BC;}_c = \dfrac{1}{|D_c|} \sum\limits_{x&#x2208;D_c} x
\\  \hat{&#x3C3;}_c^2 = \dfrac{1}{|D_c|} \sum\limits_{x&#x2208;D_c} (x-\hat{&#x3BC;}_c)(x-\hat{&#x3BC;}_c)^T
\end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.831752em;vertical-align:-2.165876em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.6500200000000005em;"><span style="top:-1.8999899999999998em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>&#x23A9;</span></span></span><span style="top:-1.89499em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-2.18999em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-2.20499em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-3.15001em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>&#x23A8;</span></span></span><span style="top:-4.2950099999999996em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-4.59001em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-4.60501em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-4.90002em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>&#x23A7;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:2.15002em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.665876em;"><span style="top:-4.665876em;"><span class="pstrut" style="height:3.32144em;"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">&#x3BC;</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord">^</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">&#x2223;</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="mrel mtight">&#x2208;</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em;"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.094436em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">x</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.32144em;"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">&#x3C3;</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">&#x2223;</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="mrel mtight">&#x2208;</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em;"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.094436em;"><span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">&#x3BC;</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord">^</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">&#x3BC;</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord">^</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:2.165876em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p>&#x8BE5;&#x65B9;&#x6CD5;&#x4F30;&#x8BA1;&#x7ED3;&#x679C;&#x7684;&#x51C6;&#x786E;&#x6027;&#x4E25;&#x91CD;&#x4F9D;&#x8D56;&#x6240;&#x5047;&#x8BBE;&#x7684;&#x6982;&#x7387;&#x5206;&#x5E03;&#x662F;&#x5426;&#x7B26;&#x5408;&#x6F5C;&#x5728;&#x7684;&#x771F;&#x5B9E;&#x6570;&#x636E;&#x7684;&#x5206;&#x5E03;&#x3002;</p>
<h2 class="mume-header" id="%E6%9C%B4%E7%B4%A0%E8%B4%9D%E5%8F%B6%E6%96%AF">&#x6734;&#x7D20;&#x8D1D;&#x53F6;&#x65AF;</h2>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>c</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mfrac><munderover><mo>&#x220F;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mi>P</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>c</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(c \bold{\ |\ } x) = \dfrac{P(c) &#x22C5; P(x \bold{\ |\ } c)} {P(x)} = 
    \dfrac{P(c)}{P(x)}
    \prod_{i=1}^{d} P(x_i \bold{\ \vert\ } c)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">c</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.1137820000000005em;vertical-align:-1.277669em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8361130000000003em;"><span style="top:-1.872331em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x220F;</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.277669em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">c</span><span class="mclose">)</span></span></span></span></span></p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi></mrow><annotation encoding="application/x-tex">d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">d</span></span></span></span>&#xFF1A;&#x5C5E;&#x6027;&#x6570;&#x76EE;</li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">x_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>&#xFF1A;&#x7B2C;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathdefault">i</span></span></span></span>&#x4E2A;&#x5C5E;&#x6027;&#x7684;&#x53D6;&#x503C;</li>
</ul>
<h3 class="mume-header" id="%E5%9F%BA%E6%9C%AC%E6%80%9D%E6%83%B3">&#x57FA;&#x672C;&#x601D;&#x60F3;</h3>

<p>&#x5C5E;&#x6027;&#x6761;&#x4EF6;&#x72EC;&#x7ACB;&#x6027;&#x5047;&#x8BBE;&#x3002;</p>
<h4 class="mume-header" id="example">Example</h4>

<table>
<thead>
<tr>
<th>Ca+</th>
<th>Mg+</th>
<th>Na+</th>
<th>Cl-</th>
<th>Type</th>
</tr>
</thead>
<tbody>
<tr>
<td>&#x4F4E;</td>
<td>&#x9AD8;</td>
<td>&#x9AD8;</td>
<td>&#x9AD8;</td>
<td>&#x51B0;&#x5DDD;&#x6C34;</td>
</tr>
<tr>
<td>&#x9AD8;</td>
<td>&#x4F4E;</td>
<td>&#x9AD8;</td>
<td>&#x9AD8;</td>
<td>&#x51B0;&#x5DDD;&#x6C34;</td>
</tr>
<tr>
<td>&#x4F4E;</td>
<td>&#x9AD8;</td>
<td>&#x4F4E;</td>
<td>&#x4F4E;</td>
<td>&#x51B0;&#x5DDD;&#x6C34;</td>
</tr>
<tr>
<td>&#x9AD8;</td>
<td>&#x9AD8;</td>
<td>&#x4F4E;</td>
<td>&#x4F4E;</td>
<td>&#x51B0;&#x5DDD;&#x6C34;</td>
</tr>
<tr>
<td>&#x4F4E;</td>
<td>&#x4F4E;</td>
<td>&#x4F4E;</td>
<td>&#x4F4E;</td>
<td>&#x6E56;&#x6CCA;&#x6C34;</td>
</tr>
<tr>
<td>&#x9AD8;</td>
<td>&#x4F4E;</td>
<td>&#x4F4E;</td>
<td>&#x4F4E;</td>
<td>&#x6E56;&#x6CCA;&#x6C34;</td>
</tr>
<tr>
<td>&#x4F4E;</td>
<td>&#x9AD8;</td>
<td>&#x9AD8;</td>
<td>&#x4F4E;</td>
<td>&#x6E56;&#x6CCA;&#x6C34;</td>
</tr>
<tr>
<td>&#x9AD8;</td>
<td>&#x4F4E;</td>
<td>&#x9AD8;</td>
<td>&#x4F4E;</td>
<td>&#x6E56;&#x6CCA;&#x6C34;</td>
</tr>
<tr>
<td>&#x4F4E;</td>
<td>&#x9AD8;</td>
<td>&#x9AD8;</td>
<td>&#x4F4E;</td>
<td>?</td>
</tr>
</tbody>
</table>
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><msup><mi>a</mi><mo lspace="0em" rspace="0em">+</mo></msup><mo>=</mo><mtext>&#x4F4E;</mtext><mo separator="true">,</mo><mi>M</mi><msup><mi>g</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x9AD8;</mtext><mo separator="true">,</mo><mi>N</mi><msup><mi>a</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x9AD8;</mtext><mo separator="true">,</mo><mi>C</mi><msup><mi>l</mi><mo>=</mo></msup><mtext>&#x4F4E;</mtext><mrow><mtext>&#xA0;</mtext><mo fence="false">&#x2223;</mo><mtext>&#xA0;</mtext></mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mtext>&#x51B0;&#x5DDD;&#x6C34;</mtext><mo stretchy="false">)</mo><mo>&#xD7;</mo><mi>P</mi><mo stretchy="false">(</mo><mtext>&#x51B0;&#x5DDD;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(Ca^{+}=&#x4F4E;,Mg^+=&#x9AD8;,Na^+=&#x9AD8;,Cl^=&#x4F4E; {\ \big|\ } Type=&#x51B0;&#x5DDD;&#x6C34;) &#xD7; P(&#x51B0;&#x5DDD;&#x6C34;)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.021331em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">+</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.9657709999999999em;vertical-align:-0.19444em;"></span><span class="mord cjk_fallback">&#x4F4E;</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.9657709999999999em;vertical-align:-0.19444em;"></span><span class="mord cjk_fallback">&#x9AD8;</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.21799em;vertical-align:-0.35000999999999993em;"></span><span class="mord cjk_fallback">&#x9AD8;</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6198089999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mrel mtight">=</span></span></span></span></span></span></span></span><span class="mord cjk_fallback">&#x4F4E;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8679800000000001em;"><span style="top:-2.2559899999999997em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.26698em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000999999999993em;"><span></span></span></span></span></span></span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord cjk_fallback">&#x51B0;</span><span class="mord cjk_fallback">&#x5DDD;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord cjk_fallback">&#x51B0;</span><span class="mord cjk_fallback">&#x5DDD;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span></span><br>
<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.15999999999999992em" columnalign="left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">=</mo></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><msup><mi>a</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x4F4E;</mtext><mrow><mtext>&#xA0;</mtext><mo fence="false">&#x2223;</mo><mtext>&#xA0;</mtext></mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mtext>&#x51B0;&#x5DDD;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">&#xD7;</mo></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>M</mi><msup><mi>g</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x9AD8;</mtext><mrow><mtext>&#xA0;</mtext><mo fence="false">&#x2223;</mo><mtext>&#xA0;</mtext></mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mtext>&#x51B0;&#x5DDD;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">&#xD7;</mo></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>N</mi><msup><mi>a</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x9AD8;</mtext><mrow><mtext>&#xA0;</mtext><mo fence="false">&#x2223;</mo><mtext>&#xA0;</mtext></mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mtext>&#x51B0;&#x5DDD;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">&#xD7;</mo></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><msup><mi>l</mi><mo>&#x2212;</mo></msup><mo>=</mo><mtext>&#x4F4E;</mtext><mrow><mtext>&#xA0;</mtext><mo fence="false">&#x2223;</mo><mtext>&#xA0;</mtext></mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mtext>&#x51B0;&#x5DDD;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">&#xD7;</mo></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>P</mi><mo stretchy="false">(</mo><mtext>&#x51B0;&#x5DDD;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mrow><mo fence="true">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle><mo>&#xD7;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>3</mn><mn>4</mn></mfrac></mstyle><mo>&#xD7;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mn>4</mn></mfrac></mstyle><mo>&#xD7;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mn>6</mn></mfrac></mstyle><mo fence="true">)</mo></mrow><mo>&#xD7;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>8</mn></mfrac></mstyle><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>32</mn></mfrac></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{array}{l}
    \\  =
    \\  &amp; P(Ca^+=&#x4F4E; {\ \big|\ } Type=&#x51B0;&#x5DDD;&#x6C34;) &amp; &#xD7; 
    \\  &amp; P(Mg^+=&#x9AD8; {\ \big|\ } Type=&#x51B0;&#x5DDD;&#x6C34;) &amp; &#xD7; 
    \\  &amp; P(Na^+=&#x9AD8; {\ \big|\ } Type=&#x51B0;&#x5DDD;&#x6C34;) &amp; &#xD7; 
    \\  &amp; P(Cl^-=&#x4F4E; {\ \big|\ } Type=&#x51B0;&#x5DDD;&#x6C34;) &amp; &#xD7;
    \\  &amp; P(&#x51B0;&#x5DDD;&#x6C34;)
    \\\\    = \left(
        \dfrac{1}{2} &#xD7; \dfrac{3}{4} &#xD7; \dfrac{2}{4} &#xD7; \dfrac{2}{6}
    \right) &#xD7; \dfrac{4}{8} = \dfrac{1}{32}
    \end{array}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:12.11195em;vertical-align:-5.805975em;"></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.305975em;"><span style="top:-8.915975em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-7.715975em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"><span class="mrel">=</span></span></span><span style="top:-6.487995000000001em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-5.260015em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-4.032035em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-2.804054999999999em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-1.6040549999999982em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-0.4040549999999989em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:1.405945em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">8</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span><span class="mord">2</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:5.805975em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.905975em;"><span style="top:-6.0379950000000004em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x4F4E;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8679800000000001em;"><span style="top:-2.2559899999999997em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.26698em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000999999999993em;"><span></span></span></span></span></span></span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x51B0;</span><span class="mord cjk_fallback">&#x5DDD;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span><span style="top:-4.810015000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x9AD8;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8679800000000001em;"><span style="top:-2.2559899999999997em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.26698em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000999999999993em;"><span></span></span></span></span></span></span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x51B0;</span><span class="mord cjk_fallback">&#x5DDD;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span><span style="top:-3.5820349999999994em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x9AD8;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8679800000000001em;"><span style="top:-2.2559899999999997em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.26698em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000999999999993em;"><span></span></span></span></span></span></span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x51B0;</span><span class="mord cjk_fallback">&#x5DDD;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span><span style="top:-2.354054999999999em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">&#x2212;</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x4F4E;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8679800000000001em;"><span style="top:-2.2559899999999997em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.26698em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000999999999993em;"><span></span></span></span></span></span></span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x51B0;</span><span class="mord cjk_fallback">&#x5DDD;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span><span style="top:-1.154054999999998em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord cjk_fallback">&#x51B0;</span><span class="mord cjk_fallback">&#x5DDD;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:2.205945000000002em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.905975em;"><span style="top:-6.0379950000000004em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#xD7;</span></span></span><span style="top:-4.810015000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#xD7;</span></span></span><span style="top:-3.5820349999999994em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#xD7;</span></span></span><span style="top:-2.354054999999999em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#xD7;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.005945000000001em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span></span></span></span></p>
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><msup><mi>a</mi><mo lspace="0em" rspace="0em">+</mo></msup><mo>=</mo><mtext>&#x4F4E;</mtext><mo separator="true">,</mo><mi>M</mi><msup><mi>g</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x9AD8;</mtext><mo separator="true">,</mo><mi>N</mi><msup><mi>a</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x9AD8;</mtext><mo separator="true">,</mo><mi>C</mi><msup><mi>l</mi><mo>=</mo></msup><mtext>&#x4F4E;</mtext><mrow><mtext>&#xA0;</mtext><mo fence="false">&#x2223;</mo><mtext>&#xA0;</mtext></mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mtext>&#x6E56;&#x6CCA;&#x6C34;</mtext><mo stretchy="false">)</mo><mo>&#xD7;</mo><mi>P</mi><mo stretchy="false">(</mo><mtext>&#x6E56;&#x6CCA;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(Ca^{+}=&#x4F4E;,Mg^+=&#x9AD8;,Na^+=&#x9AD8;,Cl^=&#x4F4E; {\ \big|\ } Type=&#x6E56;&#x6CCA;&#x6C34;) &#xD7; P(&#x6E56;&#x6CCA;&#x6C34;)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.021331em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">+</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.9657709999999999em;vertical-align:-0.19444em;"></span><span class="mord cjk_fallback">&#x4F4E;</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.9657709999999999em;vertical-align:-0.19444em;"></span><span class="mord cjk_fallback">&#x9AD8;</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.21799em;vertical-align:-0.35000999999999993em;"></span><span class="mord cjk_fallback">&#x9AD8;</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6198089999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mrel mtight">=</span></span></span></span></span></span></span></span><span class="mord cjk_fallback">&#x4F4E;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8679800000000001em;"><span style="top:-2.2559899999999997em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.26698em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000999999999993em;"><span></span></span></span></span></span></span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord cjk_fallback">&#x6E56;</span><span class="mord cjk_fallback">&#x6CCA;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord cjk_fallback">&#x6E56;</span><span class="mord cjk_fallback">&#x6CCA;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span></span><br>
<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.15999999999999992em" columnalign="left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">=</mo></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><msup><mi>a</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x4F4E;</mtext><mrow><mtext>&#xA0;</mtext><mo fence="false">&#x2223;</mo><mtext>&#xA0;</mtext></mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mtext>&#x6E56;&#x6CCA;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">&#xD7;</mo></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>M</mi><msup><mi>g</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x9AD8;</mtext><mrow><mtext>&#xA0;</mtext><mo fence="false">&#x2223;</mo><mtext>&#xA0;</mtext></mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mtext>&#x6E56;&#x6CCA;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">&#xD7;</mo></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>N</mi><msup><mi>a</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x9AD8;</mtext><mrow><mtext>&#xA0;</mtext><mo fence="false">&#x2223;</mo><mtext>&#xA0;</mtext></mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mtext>&#x6E56;&#x6CCA;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">&#xD7;</mo></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><msup><mi>l</mi><mo>&#x2212;</mo></msup><mo>=</mo><mtext>&#x4F4E;</mtext><mrow><mtext>&#xA0;</mtext><mo fence="false">&#x2223;</mo><mtext>&#xA0;</mtext></mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mtext>&#x6E56;&#x6CCA;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">&#xD7;</mo></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>P</mi><mo stretchy="false">(</mo><mtext>&#x6E56;&#x6CCA;&#x6C34;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mrow><mo fence="true">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle><mo>&#xD7;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>4</mn></mfrac></mstyle><mo>&#xD7;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mn>4</mn></mfrac></mstyle><mo>&#xD7;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>6</mn></mfrac></mstyle><mo fence="true">)</mo></mrow><mo>&#xD7;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>8</mn></mfrac></mstyle><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>48</mn></mfrac></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{array}{l}
    \\  =
    \\  &amp; P(Ca^+=&#x4F4E; {\ \big|\ } Type=&#x6E56;&#x6CCA;&#x6C34;) &amp; &#xD7; 
    \\  &amp; P(Mg^+=&#x9AD8; {\ \big|\ } Type=&#x6E56;&#x6CCA;&#x6C34;) &amp; &#xD7; 
    \\  &amp; P(Na^+=&#x9AD8; {\ \big|\ } Type=&#x6E56;&#x6CCA;&#x6C34;) &amp; &#xD7; 
    \\  &amp; P(Cl^-=&#x4F4E; {\ \big|\ } Type=&#x6E56;&#x6CCA;&#x6C34;) &amp; &#xD7;
    \\  &amp; P(&#x6E56;&#x6CCA;&#x6C34;)
    \\\\    = \left(
        \dfrac{1}{2} &#xD7; \dfrac{1}{4} &#xD7; \dfrac{2}{4} &#xD7; \dfrac{4}{6}
    \right) &#xD7; \dfrac{4}{8} = \dfrac{1}{48}
    \end{array}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:12.11195em;vertical-align:-5.805975em;"></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.305975em;"><span style="top:-8.915975em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-7.715975em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"><span class="mrel">=</span></span></span><span style="top:-6.487995000000001em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-5.260015em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-4.032035em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-2.804054999999999em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-1.6040549999999982em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:-0.4040549999999989em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span><span style="top:1.405945em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">8</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span><span class="mord">8</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:5.805975em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.905975em;"><span style="top:-6.0379950000000004em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x4F4E;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8679800000000001em;"><span style="top:-2.2559899999999997em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.26698em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000999999999993em;"><span></span></span></span></span></span></span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x6E56;</span><span class="mord cjk_fallback">&#x6CCA;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span><span style="top:-4.810015000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x9AD8;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8679800000000001em;"><span style="top:-2.2559899999999997em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.26698em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000999999999993em;"><span></span></span></span></span></span></span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x6E56;</span><span class="mord cjk_fallback">&#x6CCA;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span><span style="top:-3.5820349999999994em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x9AD8;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8679800000000001em;"><span style="top:-2.2559899999999997em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.26698em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000999999999993em;"><span></span></span></span></span></span></span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x6E56;</span><span class="mord cjk_fallback">&#x6CCA;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span><span style="top:-2.354054999999999em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">&#x2212;</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x4F4E;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8679800000000001em;"><span style="top:-2.2559899999999997em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.26698em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000999999999993em;"><span></span></span></span></span></span></span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord mathdefault">p</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">&#x6E56;</span><span class="mord cjk_fallback">&#x6CCA;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span><span style="top:-1.154054999999998em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord cjk_fallback">&#x6E56;</span><span class="mord cjk_fallback">&#x6CCA;</span><span class="mord cjk_fallback">&#x6C34;</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:2.205945000000002em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.905975em;"><span style="top:-6.0379950000000004em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#xD7;</span></span></span><span style="top:-4.810015000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#xD7;</span></span></span><span style="top:-3.5820349999999994em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#xD7;</span></span></span><span style="top:-2.354054999999999em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#xD7;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.005945000000001em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span></span></span></span></p>
<p>&#x6545;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>C</mi><msup><mi>a</mi><mo lspace="0em" rspace="0em">+</mo></msup><mo>=</mo><mtext>&#x4F4E;</mtext><mo separator="true">,</mo><mi>M</mi><msup><mi>g</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x9AD8;</mtext><mo separator="true">,</mo><mi>N</mi><msup><mi>a</mi><mo>+</mo></msup><mo>=</mo><mtext>&#x9AD8;</mtext><mo separator="true">,</mo><mi>C</mi><msup><mi>l</mi><mo>=</mo></msup><mtext>&#x4F4E;</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(Ca^{+}=&#x4F4E;,Mg^+=&#x9AD8;,Na^+=&#x9AD8;,Cl^=&#x4F4E;)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.021331em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">+</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.9657709999999999em;vertical-align:-0.19444em;"></span><span class="mord cjk_fallback">&#x4F4E;</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.9657709999999999em;vertical-align:-0.19444em;"></span><span class="mord cjk_fallback">&#x9AD8;</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord cjk_fallback">&#x9AD8;</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6198089999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mrel mtight">=</span></span></span></span></span></span></span></span><span class="mord cjk_fallback">&#x4F4E;</span><span class="mclose">)</span></span></span></span>&#x4E3A;&#x51B0;&#x5DDD;&#x6C34;&#x3002;</p>
<h3 class="mume-header" id="%E6%9C%B4%E7%B4%A0%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%88%86%E7%B1%BB%E5%99%A8%E8%A1%A8%E8%BE%BE%E5%BC%8F">&#x6734;&#x7D20;&#x8D1D;&#x53F6;&#x65AF;&#x5206;&#x7C7B;&#x5668;&#x8868;&#x8FBE;&#x5F0F;</h3>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>h</mi><mrow><mi>n</mi><mi>b</mi></mrow></msub><mo>=</mo><munder><mo><mi mathvariant="normal">arg&#x2009;max</mi><mo>&#x2061;</mo></mo><mrow><mi>c</mi><mo>&#x2208;</mo><mi mathvariant="script">Y</mi></mrow></munder><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><munderover><mo>&#x220F;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mi>P</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>c</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">h_{nb} = 
    \argmax_{c&#x2208;\mathcal{Y}} P(c) 
        \prod_{i=1}^{d} P(x_i \bold{\ \vert\ } c)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight">b</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.1137820000000005em;vertical-align:-1.277669em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.43055999999999983em;"><span style="top:-2.161229em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mrel mtight">&#x2208;</span><span class="mord mtight"><span class="mord mathcal mtight" style="margin-right:0.08222em;">Y</span></span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop"><span class="mord mathrm">a</span><span class="mord mathrm">r</span><span class="mord mathrm" style="margin-right:0.01389em;">g</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathrm">m</span><span class="mord mathrm">a</span><span class="mord mathrm">x</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.006825em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8361130000000003em;"><span style="top:-1.872331em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x220F;</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.277669em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">c</span><span class="mclose">)</span></span></span></span></span></p>
<p><strong>&#x5148;&#x9A8C;&#x6982;&#x7387;</strong></p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mi mathvariant="normal">&#x2223;</mi><msub><mi>D</mi><mi>c</mi></msub><mi mathvariant="normal">&#x2223;</mi></mrow><mrow><mi mathvariant="normal">&#x2223;</mi><mi>D</mi><mi mathvariant="normal">&#x2223;</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">P(c) = \dfrac{|D_c|}{|D|}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord">&#x2223;</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p><strong>&#x4F3C;&#x7136;&#xFF08;&#x79BB;&#x6563;&#xFF09;</strong></p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mi mathvariant="normal">&#x2223;</mi><msub><mi>D</mi><mrow><mi>c</mi><mo separator="true">,</mo><msub><mi>x</mi><mi>i</mi></msub></mrow></msub><mi mathvariant="normal">&#x2223;</mi></mrow><mrow><mi mathvariant="normal">&#x2223;</mi><msub><mi>D</mi><mi>c</mi></msub><mi mathvariant="normal">&#x2223;</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">P(x_i \bold{\ \vert\ } c) = 
    \dfrac{|D_{c,x_i}|}{|D_c|}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">&#x2223;</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mpunct mtight">,</span><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord">&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p><strong>&#x4F3C;&#x7136;&#xFF08;&#x8FDE;&#x7EED;&#xFF09;</strong></p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>2</mn><mi>&#x3C0;</mi></mrow></msqrt><msub><mi>&#x3C3;</mi><mrow><mi>c</mi><mo separator="true">,</mo><mi>i</mi></mrow></msub></mrow></mfrac><mi>exp</mi><mo>&#x2061;</mo><mrow><mo fence="true">(</mo><mo>&#x2212;</mo><mfrac><mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo>&#x2212;</mo><msub><mi>&#x3BC;</mi><mrow><mi>c</mi><mo separator="true">,</mo><mi>i</mi></mrow></msub><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow><mn>2</mn><msubsup><mi>&#x3C3;</mi><mrow><mi>c</mi><mo separator="true">,</mo><mi>i</mi></mrow><mn>2</mn></msubsup></mrow></mfrac><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">P(x_i \bold{\ \vert\ } c) = 
    \dfrac{1}{\sqrt{2&#x3C0;}&#x3C3;_{c,i}}
    \exp\left(
        -
        \dfrac{
            (x_i - &#x3BC;_{c,i})^2
        }{
            2&#x3C3;_{c,i}^2
        }
    \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.2027799999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.90722em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.03588em;">&#x3C0;</span></span></span><span style="top:-2.86722em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
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M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.13278em;"><span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">&#x3C3;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.083328em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">exp</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size4">(</span></span><span class="mord">&#x2212;</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4911079999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">&#x3C3;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.795908em;"><span style="top:-2.4231360000000004em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.4129719999999999em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathdefault">&#x3BC;</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.0989719999999998em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size4">)</span></span></span></span></span></span></span></p>
<h3 class="mume-header" id="%E6%8B%89%E6%99%AE%E6%8B%89%E6%96%AF%E4%BF%AE%E6%AD%A3">&#x62C9;&#x666E;&#x62C9;&#x65AF;&#x4FEE;&#x6B63;</h3>

<p>&#x82E5;&#x67D0;&#x4E2A;&#x5C5E;&#x6027;&#x503C;&#x5728;&#x8BAD;&#x7EC3;&#x96C6;&#x4E2D;&#x6CA1;&#x6709;&#x4E0E;&#x67D0;&#x4E2A;&#x7C7B;&#x540C;&#x65F6;&#x51FA;&#x73B0;&#x8FC7;&#xFF0C;&#x5219;&#x76F4;&#x63A5;&#x8BA1;&#x7B97;&#x4F1A;&#x51FA;&#x73B0;&#x95EE;&#x9898;&#xFF0C;&#x4E3A;&#x4E86;&#x907F;&#x514D;&#x5176;&#x5B83;&#x5C5E;&#x6027;&#x643A;&#x5E26;&#x7684;&#x4FE1;&#x606F;&#x88AB;&#x8BAD;&#x7EC3;&#x96C6;&#x4E2D;&#x672A;&#x51FA;&#x73B0;&#x7684;&#x5C5E;&#x6027;&#x503C;&#x62B9;&#x53BB;&#xFF0C;&#x5728;&#x4F30;&#x8BA1;&#x6982;&#x7387;&#x65F6;&#x9700;&#x8981;&#x8FDB;&#x884C;<strong>&#x62C9;&#x666E;&#x62C9;&#x65AF;&#x4FEE;&#x6B63;</strong>&#x3002;</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mi mathvariant="normal">&#x2223;</mi><msub><mi>D</mi><mrow><mi>c</mi><mo separator="true">,</mo><msub><mi>x</mi><mi>i</mi></msub></mrow></msub><mi mathvariant="normal">&#x2223;</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi mathvariant="normal">&#x2223;</mi><msub><mi>D</mi><mi>c</mi></msub><mi mathvariant="normal">&#x2223;</mi><mo>+</mo><msub><mi>N</mi><mi>i</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">P(x_i \bold{\ \vert\ } c) = \dfrac{|D_{c,x_i}| + 1}{|D_c| + N_i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">&#x2223;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mpunct mtight">,</span><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord">&#x2223;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h2 class="mume-header" id="%E5%8D%8A%E6%9C%B4%E7%B4%A0%E8%B4%9D%E5%8F%B6%E6%96%AF">&#x534A;&#x6734;&#x7D20;&#x8D1D;&#x53F6;&#x65AF;</h2>

<p>&#x4E00;&#x822C;&#x60C5;&#x51B5;&#x4E0B;&#xFF0C;&#x5C5E;&#x6027;&#x6761;&#x4EF6;&#x72EC;&#x7ACB;&#x6027;&#x5047;&#x8BBE;&#x5F88;&#x96BE;&#x6210;&#x7ACB;&#xFF0C;&#x5C1D;&#x8BD5;&#x5BF9;&#x8BE5;&#x6761;&#x4EF6;&#x8FDB;&#x884C;&#x4E00;&#x5B9A;&#x7684;&#x653E;&#x677E;&#xFF0C;&#x5F97;&#x5230;&#x534A;&#x6734;&#x7D20;&#x8D1D;&#x53F6;&#x65AF;&#x5206;&#x7C7B;&#x5668;&#x5B66;&#x4E60;&#x65B9;&#x6CD5;&#x3002;</p>

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